Factor by grouping. 4y^3+3y^2+8y+6 square

To factor the polynomial \(4y^3 + 3y^2 + 8y + 6\) by grouping, follow these steps:<br /><br />1. **Group the terms**: Divide the polynomial into two groups.<br /> \[<br /> (4y^3 + 3y^2) + (8y + 6)<br /> \]<br /><br />2. **Factor out the greatest common factor (GCF) from each group**:<br /> - From the first group \((4y^3 + 3y^2)\), factor out \(y^2\):<br /> \[<br /> y^2(4y + 3)<br /> \]<br /> - From the second group \((8y + 6)\), factor out \(2\):<br /> \[<br /> 2(4y + 3)<br /> \]<br /><br />3. **Combine the factored groups**:<br /> Now we have:<br /> \[<br /> y^2(4y + 3) + 2(4y + 3)<br /> \]<br /><br />4. **Factor out the common binomial factor \((4y + 3)\)**:<br /> \[<br /> (4y + 3)(y^2 + 2)<br /> \]<br /><br />So, the factored form of the polynomial \(4y^3 + 3y^2 + 8y + 6\) is:<br />\[<br />(4y + 3)(y^2 + 2)<br />\]